how to calculate the probability of a poisson distribution in matlab

To calculate the probability of a Poisson distribution in Matlab, you can use the poisspdf function. This function takes two inputs: the value(s) at which you want to calculate the probability, and the mean of the Poisson distribution.

Here's an example usage:

main.m
lambda = 3.5;  % the mean of the Poisson distribution
x = 2;         % the value at which we want to calculate the probability

prob = poisspdf(x, lambda);
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This will give you the probability of observing exactly x events in a Poisson process with mean lambda. If you want to calculate the probability of observing x or fewer (or x or more) events, you can use the poisscdf function instead:

main.m
prob_less_than_two = poisscdf(2, lambda);
prob_more_than_two = 1 - poisscdf(2, lambda);  % probability of 2 or more events
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Again, lambda is the mean of the Poisson distribution, and 2 is the value we're interested in. The poisscdf function calculates the cumulative distribution function (CDF) of the Poisson distribution, so prob_less_than_two will give us the probability of observing 0 or 1 events, and prob_more_than_two will give us the probability of observing 2 or more events.